Question

analyze the graph of the exponential decay function the initial value is the base, or rate of change, is the domain is

Explanation:

Step1: Identify initial value

The initial value of an exponential function is the y-value when $x=0$. From the graph, the point $(0,1)$ gives this value.

Step2: Find the base (decay factor)

Use the general exponential form $y = a(b)^x$, where $a=1$ (initial value). Substitute $(1,\frac{1}{3})$:
$\frac{1}{3} = 1 \cdot b^1$
Solve for $b$: $b = \frac{1}{3}$

Step3: Determine the domain

Exponential functions are defined for all real numbers, so the domain is all real $x$.

Answer:

The initial value is $\boldsymbol{1}$
The base, or rate of change, is $\boldsymbol{\frac{1}{3}}$
The domain is $\boldsymbol{(-\infty, \infty)}$ (all real numbers)